gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification

Abstract

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a k-nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658x speed-up with 1 to 5% relative errors.

References in corpus (11)

• Discovering Symbolic Models from Deep Learning with Inductive Biases
• A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
• Data-driven reduced-order models via regularized operator inference for a single-injector combustion process
• Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
• LaSDI: Parametric Latent Space Dynamics Identification
• Deep autoencoders for physics-constrained data-driven nonlinear materials modeling
• Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques
• Component-wise reduced order model lattice-type structure design
• Domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) nonlinear model reduction
• Reduced order models for Lagrangian hydrodynamics
• Efficient space-time reduced order model for linear dynamical systems in Python using less than 120 lines of code

Cited by in corpus (10)

• GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder
• Gappy AE: A Nonlinear Approach for Gappy Data Reconstruction using Auto-Encoder
• Physics-informed active learning with simultaneous weak-form latent space dynamics identification
• Evaluating the Stability of Deep Learning Latent Feature Spaces
• Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Method
• A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs
• Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces
• Projection-based model-order reduction via graph autoencoders suited for unstructured meshes
• Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives
• Hyper-reduction-free reduced-order Newton solvers for projection-based model-order reduction of nonlinear dynamical systems